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    <title>ltitr</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>ltitr</b> -  discrete time response (state space)  </p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[X]=ltitr(A,B,U,[x0])   </tt>
      </dd>
      <dd>
        <tt>[xf,X]=ltitr(A,B,U,[x0])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A,B</b>
        </tt>: real  matrices of appropriate dimensions</li>
      <li>
        <tt>
          <b>U,X</b>
        </tt>: real  matrices</li>
      <li>
        <tt>
          <b>x0,xf</b>
        </tt>: real vectors (default value=0 for <tt>
          <b>x0</b>
        </tt>))</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    calculates the time response of the discrete time system</p>
    <pre>

         x[t+1] = Ax[t] + Bu[t].
   
    </pre>
    <p>
    The inputs <tt>
        <b>ui</b>
      </tt>'s are the columns of the <tt>
        <b>U</b>
      </tt> matrix</p>
    <pre>

        U=[u0,u1,...,un];
   
    </pre>
    <p>
      <tt>
        <b>x0</b>
      </tt> is the vector of initial state (default value : 0) ;</p>
    <p>
      <tt>
        <b>X</b>
      </tt> is the matrix of outputs (same number of columns as <tt>
        <b>U</b>
      </tt>).</p>
    <pre>

        X=[x0,x1,x2,...,xn] 
   
    </pre>
    <p>
      <tt>
        <b>xf</b>
      </tt> is the vector of final state <tt>
        <b>xf=X[n+1]</b>
      </tt>
    </p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=eye(2,2);B=[1;1];
x0=[-1;-2];
u=[1,2,3,4,5];
x=ltitr(A,B,u,x0)
x1=A*x0+B*u(1)
x2=A*x1+B*u(2)
x3=A*x2+B*u(3) //....
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="rtitr.htm">
        <tt>
          <b>rtitr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="flts.htm">
        <tt>
          <b>flts</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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